This invention is in the field of oil and gas production. Embodiments of this invention are more specifically directed to the production performance analysis of wells for purposes of well and reservoir management.
The current economic climate emphasizes the need for optimizing hydrocarbon production. Such optimization is important considering that the costs of drilling of new wells and operating existing wells are high by historical standards, largely because of the extreme depths to which new producing wells must be drilled and because of other physical barriers to discovering and exploiting reservoirs. These high economic stakes demand operators to devote substantial resources toward effective management of oil and gas reservoirs, and effective management of individual wells within production fields.
As is well known in the modern oil and gas industry, large reservoirs of natural gas yet remain in so-called “tight” formations, in which the flow of gas into a production well is greatly restricted by the nature of the gas-bearing rock. These low permeability formations include tight sands, gas shales and gas coals. Gas shale, for example, is relatively old (e.g., Paleozoic) rock, in which the porosity and permeability has been greatly reduced over time due to compaction, cementation, recrystallization, and chemical changes over time. Permeability of gas shales and other tight reservoir rocks can be as low as in the nanodarcy range. Even though a large amount of gas is retained in the earth in these tight formations, the extremely low permeability of these formations results in very low gas production, because the low permeability restricts the rate at which formation gas away from the wellbore can travel to perforations of conventional production wells.
Hydraulic fracturing (“fracing” or “fracking”) of the formation around a wellbore is a common technique for increasing production from these tight gas formations. Typical hydraulic fracturing involves the pumping of fluid, typically water and often some chemicals, under pressure through the wellbore and into the formation. The pressure of the fluid, along with the chemical action of any chemical additives present in the fluid, cause the surrounding formation to fracture, with the line of the fracture extending from the wellbore at each perforation. The crack created by the fracture can extend on the order of hundreds of feet from the wellbore, but is typically quite narrow. Proppants, in the form of particles of silicas or sands of a selected size and composition, are typically pumped into the fracture via the wellbore, to ensure that the fracture does not close upon release of the fluid pressure. The fractures thus extend the reach of the wellbore into the formation, by providing one or more paths of high gas conductivity for a significant distance from the wellbore into the formation.
In many modern tight gas formations such as gas shales, the combination of horizontal drilling with hydraulic fracturing has proven beneficial. Horizontal wellbores can extend for a mile or more within the gas shale. In addition, because the gas shale and sand properties are generally anisotropic from the standpoint of internal strain, the drilled path will generally travel into the shale along a direction of least strain, facilitating both the penetration rate and also the eventual production following fracing.
As in any production field, the optimization of gas production from a tight gas reservoir involves decisions regarding the number and placement of wells, including whether to add or shut-in wells. In particular, well spacing in the development of a tight gas field is especially important, given the significant drilling cost typically associated with these reservoirs, and also considering the relative difficulty of obtaining good production from tight gas formations. In conventional (i.e., non-tight) reservoirs, a single well will produce from a relatively large portion of the reservoir, such that an additional well placed near an existing production well may not significantly increase production over the life of the reservoir. Conversely, because wells in tight gas formations produce from a much smaller projected region, close well spacing may be desirable to optimally produce from such gas bearing formation. Knowledge of the reservoir and its behavior is important in determining the optimal well spacing in such a field.
In addition, secondary and tertiary recovery operations, for example involving the injection of water or gas into the reservoir, involve decisions regarding whether to initiate or cease such operations, how many wells are to serve as injection wells, and where to place those wells in the field. Some wells may require well treatment, such as additional fracturing of the wellbore if drilling and production activity have plugged the wellbore surface to the extent that production has slowed. In some cases, production may be improved by shutting-in one or more wells for an extended period of time, in which case the optimization of production may require reconfiguring the entire production field. All of these actions are performed with an eye toward maximizing production at minimum cost. As evident from these examples, the optimization of a production field is a complex problem, involving many variables and presenting many choices.
The manner in which downhole pressure and flow rate evolve over time provides insight into the reservoir pressure in the region around the well. Reservoir pressure is an important parameter in understanding the reservoir and how to optimize production, because the rate at which gas will flow into the wellbore downhole (and thus out of the well at the surface) strongly depends on the difference between the reservoir pressure and the back pressure exerted by the fluid in the wellbore. Over time, the volume of gas drawn out of the well will generally reduce the reservoir pressure, and the rate of production will fall.
Despite all of the limitations to measurement of reservoirs and sub-surface properties, reservoir management decisions must still be made, and therefore will be made using the best available yet incomplete understanding of the structure of the reservoir. As mentioned above, these reservoir management decisions include whether and where to place additional production wells, whether and where to inject gas or other substances for secondary recovery operations, and the like. Well management decisions, such as whether, when, and how to work over an existing production well to improve its production output, must also be made, even if based on a limited understanding of the reservoir. And, of course, short-term and long-term economic analysis of the reservoir is also important to the operator and the financial backers of the project.
In order to make these decisions, reservoir engineers commonly develop models of reservoir behavior. Conventional reservoir models are based on seismic and other geological surveys of the production field, along with conclusions that can be drawn from well logs, pressure transient analysis, and the like. These models are applied to conventional reservoir “simulator” computer programs, by way of which the reservoir engineer can analyze the behavior of the reservoir under production conditions, and by way of which the engineer can simulate the behavior of the reservoir in response to potential reservoir management actions (i.e., “what-if” analysis). Some reservoir simulators approximate fluid flow in the reservoir on a grid of geometric elements, and numerically simulate fluid flow behavior using finite-difference or finite-element techniques to solve for pressure and flow conditions within and between elements in the grid. Simulation of the reservoir behavior is then attained by stepping in time and evolving the inter-element flows and the pressures at each grid element over a sequence of the time steps.
The use of finite-difference modeling to simulate the behavior of a relatively large production field over time utilizes the “gridding” of the three-dimensional subsurface volume into incremental volume blocks, or cells, within the overall grid. In a typical model for fluid flow in the subsurface, rock properties pertaining to fluid conductivity are assigned to each grid cell. Examples of these properties include porosity and permeability, as based on core samples, well logs, and seismic survey data. The model is constructed from one or more functions for expressing flow out of the cell as a function of flow into the cell, and for expressing the fluid pressure within the cell. These functions in the model can then be solved simultaneously, given a set of initial conditions, using conventional computer simulation programs. Simulations of production over time from one or more wells penetrating the modeled reservoir, and of pressure distribution within the modeled reservoir over time, can lend insight into the expected behavior of the reservoir, and can evaluate various options in maximizing the production from the reservoir. For example, the economic benefit of placing a new production well at a particular location can be evaluated by way of such a simulation. The effects of other actions, such as shutting-in wells, initiating secondary recovery activities, re-working wells, etc. can similarly be evaluated.
Finite-difference models of relatively large production fields of even modest complexity can become quite large, in the number of grid cells. The computational complexity and cost of simulating the behavior of models including large numbers of grid cells can be prohibitive, even with modern high performance computer systems. As such, it is useful to reduce the number of grid cells in the model, by increasing the volume of each grid cell. For example, a typical grid cell in a reasonably manageable finite-difference model of a large production field may be on the order of 100 feet on a side. Conventional models assume the assigned properties (e.g., porosity, permeability) to be constant within each grid cell, to avoid higher-order computations.
Conventional commercially available reservoir simulation computer program packages include the VIP® reservoir simulation suite available from Halliburton, and NEXUS® reservoir simulation software, also available from Halliburton.
However, it has been observed that finite-difference models are not particularly useful to simulate the behavior of tight gas formations using conventional simulation software packages. In these tight gas formations of extremely low permeability, reservoir pressure can change dramatically within relatively small distances, such as on the order of one foot or less. The width of fractures caused by hydraulic fracturing can be even smaller yet, for example on the order of 0.1 inches. Because of these high pressure gradients over close distances in tight gas formations, the relatively coarse grid cells typically used for large scale reservoir modeling are thus generally inaccurate. However, dramatic reduction in the size of grid cells throughout the entire reservoir will render the computational burden unrealistic.
Local grid refinement (“LGR”) is a known technique for defining grid cells as useful in finite-difference modeling. In a general sense, LGR defines fine grid cells of small size in some regions of the overall modeled volume with coarse grid cells of larger size defining other regions of the volume. For example, use of LGR in reservoir modeling has involved defining fine grid cells in the near wellbore region of a single fractured horizontal well location, in order to derive corrections for transmissibility as applied to the overall coarse grid cell model. The coarse grid cell model and fine grid cell model otherwise tend to deviate at early simulation times. The reservoir can then be modeled using coarse grid cells, to which the transmissibility corrections derived from the fine grid cells are applied, to accurately simulate production from such a well.